In gear transmission design, there is a growing demand for the seemingly opposed requirements of carrying greater loads at higher speeds, with more reliability and quietness of operation. In part, these demands may be met to some extent by improved materials, better balancing, more nearly perfect machined surfaces, and more intensive attention to a myriad of design details. Such details include stringent mathematical analysis of both the kinematic and dynamic conditions of operation.
An essential purpose of gear-tooth profiles is to transmit rotary motion from one shaft to another. In many cases, there is an additional requirement of uniform rotary motion. An almost infinite number of forms may be used as gear-tooth profiles. Although an involute profile is one of the most commonly used in conventional gear-tooth forms that are used to transmit power, occasions may arise when some other profile can be used to advantage. In all such mechanisms, even small deviations in rotational velocity can lead to poor machine performance, premature failure, and human discomfort caused by noise and vibrations in the working gears.
An ideal gear profile may be mathematically determined. Inevitably, surface deviations occur from the ideal profile. Such deviations tend to cause an excessive acceleration or deceleration of a driven gear in relation to a driving gear, which may in turn result in noise, vibration, and knocking. Such adverse effects may also be manifest in ideal gear profiles which are mounted with some degree of eccentricity.
In general, kinematic error derives from instantaneous oscillations caused by production deviations of gear members from their proper theoretical parameters. Such errors arise from an actual positioning in space in relation to where a given point on the gear profile should be if no error existed. As a kinematic process, these errors produce acceleration and deceleration or torsional vibrations of the driven output shaft of a power transmission system. Another contributing factor may be the frequency with which meshing occurs between mating teeth. In some cases, such errors could be the source of dynamic torsional effects, which manifest themselves as kinematic errors.
In the past, physical sensors have been used to measure kinematic errors of transmissions. Such sensors include encoding sensors, seismic sensors, and optical sensors. In the case of most known kinematic error measuring systems, there is a need to install sensors upon or adjacent to the gear elements to be observed. Such sensors make physical contact with the machinery under observation, require space, and may affect the error phenomenon to be observed.
Accordingly, a need has arisen for non-contacting devices which are insensitive to radial, torsional, on linear movements of transmission shafts on which sensors should be installed under observation.
At the present time, the main method of measuring kinematic accuracy is based on mounting grid optical encoders on the final shafts of transmission systems and generating cyclic electrical signals. The phase difference of the signals, which are generated at the same frequency are then observed. Such observations indicate kinematic error in the gear mechanism.
Even those measuring systems may be difficult to use because optical encoders as a rule are large and must be mounted on the shafts very precisely, perhaps with special mounting devices. Also, such encoders are sensitive to vibration and heat, besides being sensitive to runouts (i.e. small periodic displacement, or beating) of the shaft mechanism. Further, for optical encoders, the speed of shaft rotation is limited, often making it impossible to use them at working speeds to explore dynamic processes. Electronic systems based on phase-measurement principles could control gear mechanisms with integer ratios, but measurement of automotive axles, which have as rule irrational digit ratios, may still be a technological challenge to conventional approaches.
One method of measuring torsional vibration in a rotating shaft uses a laser doppler velocimeter (LDV). One such LDV is available from the Bruel & Kjaer Company (Denmark) (Model 2523). This system allows an observer to measure torsional vibration of a rotating shaft by receiving a signal indicative of the deviation of instantaneous surface velocity from an average level.
One of the co-inventors of the present invention is the author of Russian Reference No. I966733, which discloses a seismic device that contacts the machine elements under observation. One problem which was only partially solved by that approach was how to decrease the frequency of vibration of the seismic sensing unit.
Another disclosure of one of the co-inventors herein is found in Russian Reference No. 698373, which discloses an optical encoder that measures kinematic errors in chains with non-integer ratios. Again, a contacting relationship is required between the encoder and the machinery under observation.
The Proceedings of the International Conference on Motion and Power Transmissions in Hiroshima, Japan on Nov. 23-26, 1991 included a paper entitled "Measurement of Gear Transmission Error Using Laser Velocimeters", pages 225-229, which are hereby incorporated by reference. That paper discloses a gear transmission error measurement system using a laser to measure the surface speeds of objects. The system has two rotating gears having the same surface speeds. That system does not measure the angular velocities of interacting gear elements, which may rotate at different rates of angular displacement.
A new method of kinematic accuracy checking is required which would be free from such drawbacks.